Various chemical and physical parameters of a material may be of interest in fluid analysis, process monitoring, and other operations, and a variety of systems can be used to determine such parameters. For example, the index of refraction of a transparent medium may be a parameter of interest in a given operation. A critical angle measurement is one approach that can be used to obtain the index of refraction of an unknown medium.
FIG. 1 helps illustrate index of refraction, critical angle, and other related details. As shown, light rays R1, R2, & R3 pass at different angles through a first transparent medium M1 having a known refractive index n1. The light rays meet the boundary or interface between this first medium M1 and a second medium M2. In this example, the second medium M2 has an unknown index of refraction n2 that is at least less than the known refractive index n1.
A first light ray R1 passing through the first medium M1 at some angle of incidence (i.e., θi) toward the interface will have a portion that passes through the interface and refracts in the second medium M2. This first ray R1 will also have another portion that reflects off the interface back into the same medium M1. At one particular angle of incidence called the critical angle θcrit, however, an incident light ray R2 refracts parallel to the interface (i.e., an angle of 90-degrees relative to the normal of the interface) so that the refracted light passes along the boundary between the mediums M1 & M2. Light ray R3 incident at other angles θTIR beyond this critical angle θcrit will be reflected entirely in the first medium M1. This is referred to as Total Internal Reflection (TIR).
The actual value of the critical angle θcrit depends on the refractive index of the two mediums M1 & M2. Snell's Law can be used to determine the unknown index of refraction of the second medium M2 if the refractive index of M1 is known. Snell's Law is characterized as:
                    sin        ⁢                                  ⁢                  θ          1                            sin        ⁢                                  ⁢                  θ          2                      =                            v          1                          v          2                    =                        n          2                          n          1                      ,
where
θ1≡angle of incidence
θ2≡angle of refraction
v1≡light velocity in material 1
v2≡light velocity in material 2
n1≡refractive index or material 1
n2≡refractive index of material 2
At the critical angle θcrit when n1>n2
      (                  i        .        e        .            ,                                    n            2                                n            1                          <        1              )    ,the angle of incidence θ1 in the equation is the critical angle θcrit, and the angle of refraction θ2 is 90-degrees relative to the normal of the interface. By measuring the critical angle θcrit between the mediums M1 & M2 and by already knowing the refractive index n1 of the known medium M1, the unknown refractive index n2 of the second medium M2 can be calculated as: n2=n1 sin θcrit. Since the refractive index of a medium is dependent on composition, it is possible to estimate the chemical composition of M2.
Devices are known in the art that use a critical angle measurement to measure very specific chemical systems, thin films, and the like. One of the most common devices is the Abbe and Pulfrich refractometer. There are also a number of commercially available critical angle based systems for process monitoring and control. In general, none of the above-mentioned systems or classes of systems are amenable to harsh environments.
There are also other approaches to refractive index measurement, but the operating principals are sufficiently different from the critical angle methodology. As an example, refractive index can be measured by commercially available systems that include Fabry-Perot optical cavities. This type of system is not amenable to harsh environments because of thermal issues with the required electronics and fouling of the measurement region (i.e., the optical cavity) with fluids having viscosities greater than water and/or high particulate loading.
A borehole in a geological formation is an example of a harsh environment where chemical and physical parameters of materials are of interest. Various systems can be conveyed within the borehole during geophysical exploration and production operations to determine the chemical and physical parameters of materials in the borehole environs. These downhole systems can include formation testers and borehole fluid analysis systems that determine parameters of fluids or formation matrix in the vicinity of the borehole as well as materials, such as fluids, within the borehole itself. Preferably, these downhole systems make all measurements in real-time using the available instrumentation in the borehole, although data and fluids can be collected for later retrieval and processing at the surface. In analyzing the fluids, various properties of the fluid may be of interest. For example, the properties include, but are not limited to, fluid density, fluid homogeneity, salinity, gas fraction, asphaltene content, and chemical composition.
One example of such a downhole system is a formation tester tool used in the oil and gas industry to measure pressure, temperature, and other parameters of a formation penetrated by a borehole. (By definition, formation fluid is a complex mixture of liquids and/or gases.) The parametric measurements are typically combined with in-situ or uphole analyses of physical and chemical properties of the formation fluid to evaluate production prospects of reservoirs penetrated by the borehole. When conveyed downhole, the formation tester tool draws fluid into the formation tester tool for pressure measurements, analysis, sampling, and optionally for subsequent exhausting of the fluid into the borehole. Regardless of the fluid sampling methodology, accurate and precise measurements of fluid pressure and temperature are required to obtain meaningful correlations between refractive index and chemical composition.
Some borehole devices are known in the art that can measure index of refraction of a downhole fluid. However, such systems offer only limited dynamic range and resolution of measurement and suffer from other disadvantages. Furthermore, in a non-borehole environment, devices available in the art may also have a limited dynamic measurement range.